Generalized Continuum Mechanics and Engineering Applications

Generalized Continuum Mechanics and Engineering Applications

1st Edition - October 20, 2015

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  • Author: Angela Madeo
  • Hardcover ISBN: 9781785480324
  • eBook ISBN: 9780081004678

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The new concept of metamaterial is increasingly attracting the interest of physicists and mechanical engineers. Such materials are obtained by suitably assembling multiple individual elements but usually arranged in (quasi-)periodic substructures in order to show exotic global mechanical properties. Indeed, the particular shape, geometry, size, orientation and arrangement of their constituting elements can affect, the propagation of waves of light or sound in a manner not observed in natural materials, creating material properties which may give rise to unexpected engineering applications. Particularly promising in the design and description of metamaterials are those micro-structures which present high contrasts in their mechanical properties: these micro-structures, once homogenized, may produce generalized continuum media, for example, second gradient or micromorphic. Many scientific challenges related to the application of generalized continuum theories to the characterization and conception of high-performance metamaterials can be identified. In this book we identify and discuss four main potential fields of applications of generalized continuum theories, namely, mechanical behavior of fibrous composite reinforcements, wave propagation in metamaterials, mechanical behavior of concrete and mechanically driven remodeling of bone in presence of bio-resorbable materials. For each field, we underline how the use of a generalized continuum theory can be of help for describing how the presence of microstructure can affect the global mechanical behavior of the considered metamaterials.

Key Features

  • Covers four main fields of the application of continuum theories
  • Learn how to apply generalised continuum theory to describe the effects of microstructure on the mechanical behavior of materials
  • Decipher the material properties which aid your engineering applications


Industry practitioners, academics and students in the fields of mechanical and civil engineering, as well as those studying materials science, geology and geophysics, and biomechanics.

Table of Contents

    • Acknowledgments
    • 1: General Introductory Aspects
      • Abstract
      • 1.1 Introduction
      • 1.2 Generalized continuum theories and some possible applications
      • 1.3 Woven fibrous composite reinforcements
      • 1.4 Wave propagation in metamaterials
      • 1.5 Reconstructed bone remodeling
      • 1.6 Microstructure-driven energy dissipation in concrete
    • 2: Fibrous Composite Reinforcements
      • Abstract
      • 2.1 Woven fibrous composite reinforcements modeled as second gradient materials
      • 2.2 Kinematics
      • 2.3 Second gradient energy density for 3D interlocks
      • 2.4 Constitutive choice for the first gradient energy
      • 2.5 Constitutive choice for the second gradient energy
      • 2.6 Least action principle and principle of virtual powers
      • 2.7 Numerical simulations for three point bending of composite interlocks
      • 2.8 Bias extension test
      • 2.9 Numerical simulations
      • 2.10 Conclusions
    • 3: Wave Propagation in Generalized Continua
      • Abstract
      • 3.1 Band gaps in the relaxed micromorphic continuum
      • 3.2 Reflection and transmission of waves at discontinuity surfaces in second gradient continua
      • 3.3 Conclusions
    • 4: Remodeling of Bone Reconstructed with Bio-resorbable Materials
      • Abstract
      • 4.1 Generalized continuum theories for bone remodeling in the presence or absence of biomaterial
      • 4.2 A continuum two-solid mixture model for reconstructed bone remodeling
      • 4.3 A simple one-dimensional, linearized, isotropic problem
      • 4.4 Numerical simulations
      • 4.5 Conclusions
    • 5: Energy Dissipation in Modified and Unmodified Concrete
      • Abstract
      • 5.1 A simple generalized continuum model for microstructure-related friction
      • 5.2 Numerical simulations: specimen in pure compression
      • 5.3 Conclusions
    • Bibliography
    • Index

Product details

  • No. of pages: 146
  • Language: English
  • Copyright: © ISTE Press - Elsevier 2015
  • Published: October 20, 2015
  • Imprint: ISTE Press - Elsevier
  • Hardcover ISBN: 9781785480324
  • eBook ISBN: 9780081004678

About the Author

Angela Madeo

Affiliations and Expertise

INSA-Lyon, France

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